Apparently Mama Cosma was not aware that Cosmo and Wanda were married for 9895 years until this episode.

Allusions

Siegfried & Roy - The lightpole on the corner where Timmy and Wanda appear have two signs that says "Siegfried" and "Roy" making a reference to the famous entertainers and magicians.

The title is a combination of the words "Apart" and "partnership".

Goofs

Cookie twice

Cupid doesn't have the arrow

In Birthday Bashed, Timmy's birthday and his parents' anniversary are on the same day, but Cosmo and Wanda's anniversary is not on the same date.

Cosmo took one of the cookies but before Timmy and Wanda shouts "Cosmo" all the cookies were in the metal plate and Cosmo has the one he took.

When Wanda was sitting during the game show, Cupid shot a toilet scrubber into her mouth. But when the camera zoomed out to Cupid, she is seen with a plunger covering her mouth, like the other times, instead of a scrubber.

Cosmo' polystyrene tux is gone after the cat attacks him.

It is unknown how Timmy gets back into his human form since Wanda or Cosmo doesn't transform him into a human again.

The toilet scrubber on Wanda's mouth disappears and reappers.

In one scene, Cupid' golden arrow disappears from his butt.

The watch in which Timmy saw the hour was not on his hand until that point.

Fairies aren't allowed to poof up money as that's counterfeiting, but Mama Cosma keeps poofing up bags and bags of money for Cupid. Unless the money was Mama Cosma's, she shouldn't have been able to do this.

In this episode Wanda said she can't do magic without Cosmo. However in this episode she was able to turn Cosmo into things during the magic fight.

Also in multiple other episodes, Cosmo and Wanda do magic just fine without each other or when they are separated, an example is the episode "Dog's Day Afternoon".